Chapter 4, Problem 40E

Explanation of Solution

Three ways to represent an NAND gate:

• A gate is a device which is used to perform the basic logical operation.
• It accepts one or more input signals and produces the single output signal.
• It contains the three types of methods to represent the processing of gates. They are:
  • Boolean expressions
  • Logic diagrams
  • Truth tables
• It contains several types of gates. The most common types are:
  • NOT gate
  • AND gate
  • OR gate
  • XOR gate
  • NAND gate
  • NOR gate
• NAND gate:
  • An NAND gate is represented in three ways:
  • The “Boolean expression” for NAND gate:
    • No specific symbol is used to express the NAND operation.
    • The expression for NAND is the negation of an AND operation.

$\text{X = (A }·\text{ B)'}$  or   $\text{X = }\overline{\text{(A }·\text{ B)}}$

  Where A and B are the inputs and X is the output.

• The “logic diagram” for NAND gate:
  • It takes two inputs and generates a single output.

  where A and B are the inputs and X is the output.

• The “Truth table” for the NAND gate:

A	B	$\text{X =}\overline{\text{ (A }·\text{ B)}}$
0	0	1
0	1	1
1	0	1
1	1	0

• From the above truth table:
  • When both the inputs are 0, then the output is 1